As crucial rotary components of high-speed trains, wheel treads in realistic operation environment usually suffer severe cyclic shocks, which damage the health status and ultimately cause safety risks. Timely and precise health prognosis based on vibration signals is an effective technology to mitigate such risks. In this work, a new parameter-related Wiener process model is proposed to capture multiple uncertainties existed in on-site prognosis of wheel treads. The proposed model establishes a quantitative relationship between degradation rate and variations, and integrates uncertainties via heterogeneity analysis of both criterions. A maximum-likelihood-based method is presented to initialize the unknown model parameters, followed by a recursive update algorithm with fully utilization of historical lifetime information. An investigation of real-world wheel tread signals demonstrates the superiority of the proposed model in accuracy improvement.